Question

I’m trying to define an is_prime function in Haskell. Can anyone point out the issue with the use of the any function?

In addition, I know that the below code is naïve, but I am learning the language so starting with babysteps.

is_prime 0 = False
is_prime 1 = False
is_prime 2 = True
is_prime n = any [n `mod` k == 0 | k <- [2.. sqrt n]]

Answer 1

Type of any is (a -> Bool) -> [a] -> Bool, so it accepts a predicate and a collection. So you should rewrite your last case as for instance

is_prime n = not $ any (\k -> n `mod` k /= 0)
                       [2 .. ceiling $ sqrt $ fromIntegral n]

fromIntegral is necessary because sqrt‘s type is Floating a => a -> a while your n is an integer. Subsequently, without ceiling the second argument of any would be Floating t => [t]. This would break, as calling mod, whose type is Integral a => a -> a -> a, on non-integral types is illegal.

If you’d like to look for some other implementations, I can recommend for example this discussion.